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Universal approximation on non-geometric rough paths and applications to financial derivatives pricing

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  • Fabian A. Harang
  • Fred Espen Benth
  • Fride Straum

Abstract

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate It\^o integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}.

Suggested Citation

  • Fabian A. Harang & Fred Espen Benth & Fride Straum, 2024. "Universal approximation on non-geometric rough paths and applications to financial derivatives pricing," Papers 2412.16009, arXiv.org.
    • Handle: RePEc:arx:papers:2412.16009
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    File URL: http://arxiv.org/pdf/2412.16009
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